Restrained Beams
In addition to the equations of static equilibrium, relations from the geometry of elastic curve are essential to the study of indeterminate beams. Such relations can be obtained from the study of deflection and rotation of beam. This section will focus on two types of indeterminate beams; the propped beams and the fully restrained beams.
Continuous beams are those that rest over three or more supports, thereby having one or more redundant support reactions.
These section includes
1. Generalized form of three-moment equation
2. Factors for three-moment equation
3. Application of the three-moment equation
4. Reactions of continuous beams
5. Shear and moment diagrams of continuous beams
6. Continuous beams with fixed ends
7. Deflection determined by three-moment equation
8. Moment distribution method
The three-moment equation gives us the relation between the moments between any three points in a beam and their relative vertical distances or deviations. This method is widely used in finding the reactions in a continuous beam.
Consider three points on the beam loaded as shown.
Problem 713
Determine the end moment and midspan value of EIδ for the restrained beam shown in Fig. PB-010. (Hint: Because of symmetry, the end shears are equal and the slope is zero at midspan. Let the redundant be the moment at midspan.)
Problem 12
Determine the moment and maximum EIδ for the restrained beam shown in Fig. RB-012. (Hint: Let the redundants be the shear and moment at the midspan. Also note that the midspan shear is zero.)